I wouldn't recommend it, any results you have you should still be questioning if this is an effect of the RTase being at room temp.... therefore it is better to get some more, rather than waste time wondering if your results are correct. General rule: If in doubt, throw it out.

Alexander Fleming - “It may be - usually is, in fact - a false alarm that leads to nothing, but it may on the other hand be the clue provided by fate to lead you to some important advance.”

However, despite this - I am sure you would still discard a contaminated cell line, or a solution that has precipitated during storage, or something that has been stored incorrectly (as in the OP's question)...

one of the Transplant Anti-Rejection Medications (Cyclosporine ) was discovered by chance because a PhD or a PostDoc(I am not sure) saw a contamination in cell culture and he observed the effects of that fungus in cell culture.
He showed it to some PIs and his colleagues but they told him to throw it away because it is a simple contamination.

I think what you are talking about is actually two entirely different things. It's one thing not to instantly throw away an experiment that has gone wrong but make careful observations and possibly discover something new and unexpected (like in Fleming's case), I second that it's always important to observe when something turns out differently. However, this does not mean one should use a material gone bad in one's experiments on purpose - this is more likely a waste of time than leading to a new discovery.